.. s NASA TECHNICAL NOTE NASA TN D-2717 I h c cy 7 (ACCESSION NUMBER) (THRUI = i /q /> *. IPAOESI ICODE t 45 mi 2J 4 INASA CR OR TMX OR AD NUMBER) ICATEOORYI GPO PRICE $ z ' OTS PRICEIS) $ Hard copy (HC) Microfiche (MF) EXPERIMENTS ON INDUCTIVE AND CAPACITIVE RADIOFREQUENCY HEATING OF A HYDROGEN PLASMA IN A MAGNETIC FIELD by Clyde C. Swett Lewis Research Center Clevekznd, Ohio NATIONAL AERONAUTICS AND SPACE ADM NISTRATION WASH NGTON, D. C. MARCH 1965 * I NASA TN ~-2m L EXPERIMENTS ON INDUCTIVE AND CAPACITIVE RADIOFREQUENCY HEATING OF A HYDROGEN PLASMA IN A MAGNETIC FIELD By Clyde C. Swett Lewis Research Center Cleveland, Ohio NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Office of Technical Services, Department of Commerce, Washington, D.C. 20230 -- Price $1.00 EXPEKI"TS ON INDUCTIVE AND CAPACITIVE RADIOFREQUENCY HEATING OF A HYDROGEN PLASMAIN A MAGNETIC FIELD* by Clyde C. Swett Lewis Research Center SUMMARY Experimental results for heating a plasma by a radiofrequency (rf) coil having an ungrounded electrostatic shield are analyzed by using an electric- circuit model based mainly on the geometric character of the apparatus. This model indicates that the presence of a plasma adds a "lossy" capacitor in parallel with the rf coil. Consequently, power goes into the plasma both in- ductively (Ee) and electrostatically (%!Ez). It is believed that the electro- static mode of power transfer is responsible for some anomalies noted in plasma experiments. The amount of power in each mode was calculated and shown to vary with magnetic field. The inductive power transfer increased at magnetic-field values near the atomic and molecular ion cyclotron fields, whereas the electro- static power decreased or increased depending on which parameter - power or coil voltage - was held constant. Maximum total power transfer was as high as 90 percent of the input power and occurred near the atomic and molecular ion cyclotron resonance fields. The electron-density decrease noted near the reso- nant points appeared to be related to the induction mode only. Some deficien- cies of this simple model are noted, and the importance of accurate measure- ments in this type of analysis is indicated. INTRODUCTION One of the problems that exists in the plasma physics field is that of ob- taining, in the laboratory, experimental conditions that approximate those as- sumed in theoretical analyses. For example, in the field of radiofrequency (rf coil-generated plasma waves, discrepancies between calculated and experimental results have been noted in wavelengths, in the amplitudes of wave compoments, in the absence of theoretical resonances, and in the shifts in resonant fre- quency toward low magnetic fields rather than toward high magnetic fields. These discrepancies are undoubtedly due to deficiencies in the experimental setup. * An abbreviated version of this report was presented at the American Physical Society, Division of Plasma Physics Meeting, San Diego, California, November 6-9, 1963. , As part of an rf plasma heating program at the Lewis Research Center, studies are being made of one experimental factor that may be partly responsi- , ble for the anomalies. This factor is the rf coil itself. Such a coil not only generates azimuthal electric fields but also radial and axial fields. Under certain conditions, axial electrical fields may even exist in portions of the plasma not directly under the coil. Hence, the coil is not a simple source for transferring power to a plasma. A study of how the power is transferred from the coil to the plasma by the various electric fields should indicate whether or not the coil could account for the anomalies noted. To a certain extent these fields can be controlled or altered by shields near the Coil. The simplest coil configuration that can be visualized is that in which a grounded electrostatic shield is installed between the coil and plasma. For such a configuration, only one electric field is generated - an azimuthal electric field. Experimental results that utilize this configuration are re- ported in reference 1. In other related studies, the shield was not used (refs. 2 to 6). Another possible configuration is that in which the electrostatic shield is present but ungrounded. This more complicated arrangement should result in azimuthal and radial electric fields directly underneath the shield but should eliminate the axial field directly underneath the coil. Axial fields may, however, be present in the plasma between the ends of the shield and grounded portions of the system. The axial and radial fields result from an rf voltage existing on the shield due to capacitive coupling between the coil and the shield. The present experimental program was undertaken to determine how much the power transfer could be improved by using the ungrounded electrostatic-shield configuration, since it was believed that the resulting fields would be strong and would enhance power transfer. Also, it was desired to determine if the total power could be analytically separated into two different heating modes - the induction heating mode normally associated with coils, and the capacitive or electrostatic heating mode that results from capacitive coupling between coil and shield. The most promising method for accomplishing this appeared to be by determination of an equivalent electric-circuit model of the coil-shield combination that could be used with experimental data to calculate the power distribution. SYMBOLS an coefficients of terms in eq. (2) bn coefficients of terms in eq. (3) C capacitance between coil and shield, F capacitance of equivalent network, F E peak coil voltage, V 2 . Er electric field in r-direction kS peak a-c voltage on shield E, electric field in z-direction electric field in 0-direction E0 f generator frequency, mc frequency, k mc f m I network current, amp ii complex operator L coil inductance, 3.46~10-~H c inductance of equivalent circuit, H 2 path length through plasma, cm ne electron density, electrons/cc P power from rf source, W PC power dissipated in capacitive branch of circuit, W pL power dissipated in inductive branch of circuit, PR + Pp, W pR power dissipated in coil resistance, W power dissipated by induction heating in plasma, W pP pt total power in microwave interferometer, mW power in reference arm of microwave interferometer, mW p1 p2 power in plasma arm of microwave interferometer, mW R a-c coil resistance, ohms RC resistance of capacitive branch, ohms RL resistance of inductive branch, R + Rp, ohms RP resistance in inductive branch caused by plasma, ohms R resistance of equivalent circuit, ohms e phase angle, deg ne phase angle change, deg Lu angular frequency, 2nf, 2~6.5x106 rad/sec 3 73-in. (i. d.) Heat-resistant glass ,-To McLoed gage / 8-mm microwave horn 1 / IrrLGround strap JAL Section at center Philips ionization gage plasma d-c Coils ,-l-mm Microwave horn ,-rf Coils ,-4-in. (i. d.) Heat- resistant glass tube no0 omo, I gooo do- ,-\ 0 -LIT \ - - I I I \ Filament To 6-in. gas inlet Llnstantaneous A& diffusion ShieldJ direction of rf field Pump Vacuum tube 1[7 voltmeter - Uniformity of field + 11 percent in this 2- -4 <length I I 4030M 10 0 10 20 30 40 50 60 70 Distance from center, in. Figure 1. - Configuration of ion cyclotron resonance apparatus 2 llCRA 2). BASIC EXPERIMENTAL CONFIGURATION The actual apparatus for which an electric-circuit model is to be devel- oped is shown in figure 1. A basic representation of this apparatus is shown in figure 2(a), in which only the left half is shown; the right half is iden- tical except for elimination of the plasma source. A glass tube is located in a steady axial magnetic field and has a plasma column along the axis. An rf coil is wrapped around the tube. Inside of the glass tube is an electrostatic shield split longitudinally so that an azimuthal electric field can be gener- ated inside of the shield. 4 , Magnetic field t ,Location of I I/ mirror coil 00-00 - - rf Source (a) Basic experimental configuration. IT-L L rf Coil B RL = R + Rp (b) Electric-circuit model including capacitance (c) Electric-circuit model where capacitance of equivalent of equivalent network. network is zero. p, (d) Circuit equivalent of electric-circuit model where capacitance of equivalent network is zero (part (ell. Figure 2. - Basic experimental configuration and circuit models. 5 In figure 2(b) the rf coil has been represented as an inductance L in series with the a-c resistance R of the coil. These quantities L and R , would be measured at the terminals of the coil without plasma present; that is, the effects of distributed capacitance are alrea* included in them. When plasma is present there is an additional resistance R that represents the additional induction heating load due to the plasma, tffe greater the load the larger the value of Rp. The shield is located such that there can be capaci- tive coupling between coil and shield. For simplicity, this capacitance, al- though it is actually a distributed quantity, has been assumed to have an equivalent value C between the high-voltage terminal of the coil and shield (figs. 2(a) and (b)). Because the coupling results in a voltage on the shield, there is a radial electric field between the shield and the plasma column and an axial electric field between the shield and ground so that current can flow from the coil to the shield and to ground through the plasma. Between the shield and ground there is a complicated series and parallel network of capacitances, inductances, and resistances. For example, there is capacitance between the shield and plasma column and between the shield and external structures, resistance in the weak plasma lying between the shield and the plasma column, resistance in the plasma column between the shields and the ends of the tube, and inductances in the plasma column and ground-return paths.